Poisson Definition and 441 Threads

Homework Statement The number of tornadoes per year, in Georgia, has a Poisson distribution with a mean of 2.4 tornadoes. Calculate the probability that in any given year, there will be: (i) At most 2 cases. (ii) At least one case. (iii) Calculate the probability that there will be...

Hi The question is about diseased trees in an area (Poisson process), and states that λ = 15 diseased trees in a km square. I need to calculate expected distance from a point in the square to a diseased tree. Now I thought that this means that P(diseased tree = 0) ~ Po(15) = 3.059 x 10^-7 Or...

Homework Statement Solve ##\Delta\phi = -q\delta(x)## on ##\mathbb{R}##. Correct answer: ##\phi = -\frac{q}{2}|x| + Ax + B## Homework EquationsThe Attempt at a Solution In one dimension the equation becomes ##\frac{d^2 \phi}{d x^2} = -q\delta(x)##. We integrate from ##-\infty## to ##x## to...

In a cylindrical symmetry domain ## \Phi(r,z,\alpha)=\Phi(r,z) ##. Does anyone can point me what can be found in literature to solve, even with an approximate approach, this equation? \nabla^2 \Phi(r,z)=-\frac{q}{\epsilon} \exp(-\frac{\Phi(r,z)-V}{V_t}) Where ## q, \epsilon, V ## and ## V_t ##...

Please recommend two textbooks about Poisson equation, Green's function and Green's theorem for a theoretical physics student. One is easy to read so that I can have an overall understanding of the topics, another is mathematically rigorous and has a deep and modern exploration of these topics...

Hello, I have been thinking about this problem for a while, but I can't decide how it should be tackled statistically. I wonder if you can help, please. Suppose that prostheses for hip replacement are sold mainly by 2 manufacturers, A and B. Since they started being sold 20 years ago, 100 000...

Say for example I want to see the rate of injury for firefighter vs police vs soldier. ##InjuryCount_{i}## The number of injuries recorded for the ith person over time ##T_{i} ## Time the person was followed. Varies from person to person. ##I(f)_{i}## indicator for ith person of being a...

Hello! I came across this problem: A counter near a long-lived radioactive source measures an average of 100 counts per minute. What is the probability that more than 110 counts will be recorded in a given one-minute interval? I am not sure how to do it. Applying the Poisson distribution formula...

First of all I will use L to denote lambda the parameter of the distribution. X~Poission(nL), n$\in\Bbb{N}$, Y~Poisson(mL),m$\in\Bbb{N}$ with m$\ne$n S= aX+bY a,b real constants. Given observations x and y find the maximum likelihood estimator of L. The problem is I don't know what the pmf...

Homework Statement Each week, Stéphane needs to prepare 4 exercises for the following week's homework assignment. The number of problems he creates in a week follows a Poisson distribution with mean 6.9. a. What is the probability that Stéphane manages to create enough exercises for the...

Suppose I am given some charge density profile ρ(x). Poisson's equation in 1D reads d2φ/dx2 = ρ(x)/ε Is there a simple way to see what the order of magnitude of the electrostatic potential should be from a dimensional analysis?

Dear colleagues. I have a difficulty in calculating waiting time of the first packet arriving in a buffer using aggregation. Arrival follow Poisson process with rate lambda and the aggregation is done for a maximum 'm' packets or with the expiry of timer T_maximum. Can anyone help me how to...

Hi all , Could you please help me solve Poisson equation in 2D for heat transfer with Dirichlet and Neumann conditions analytically? Thank you

Homework Statement On average, 2 students per hour come into the class. What is the probability that the time between two consecutive arrivals is in the interval <10 minutes; 50 minutes>. Homework Equations p(k)=P(Y=k)=((lambda*t)k*(e-lambda*t)/k! The Attempt at a Solution I've tried using...

hi everyone initially I really want to put into words that there is absolutely no source related to following probability in poisson process and distribution $$P(S^1_A<S^1_B<S^1_C)$$ or $$P(S^n_A<S^m_B<S^k_C)$$ where $$S^1_A = \text{first arrival of A event}, S^1_B= \text{first arrival of B...

Hi guys, I have a question about computing conditional probabilities of a Poisson distribution. Say we have a Poisson distribution P(X = x) = e^(−λ)(λx)/(x!) where X is some event. My question is how would we compute P(X > x1 | X > x2), or more specifically P(X> x1 ∩ X > x2) with x1 > x2? I...

please am new here and i need a help, i can use poisson distribution to get a probability but how can i use it to get several outcome? like over and under ,1x2? thanks

guys, I have a very ımportant question. First let me introduce parameters: $$S^A_1 = \text{first arrival of A event}, and S^B_1= \text{first arrival of B event}, and S^C_1=\text{ first arrival of C event}$$, then probability of $$P(S^A_1<S^B_1) = \frac {\lambda_A} {\{ \lambda_A + \lambda_B \}...

Hello. Given a range of time in which an event can occur an indefinite number of times, we say a random variable X folows a poisson distribution when it follows this statements: X is the number of times an event occurs in an interval and X can take values 0, 1, 2, … The occurrence of one event...

Three conditions must be met in order for the Poisson Distribution to be used: 1) The average count rate is constant over time 2) The counts occurring are independent 3) The probability of 2 or more counts occurring in the interval $n$ is zero Simply, why must these conditions be met for valid...

I am trying to solve the poisson equation with neumann BC's in a 2D cartesian geometry as part of a Navier-Stokes solver routine and was hoping for some help. I am using a fast Fourier transform in the x direction and a finite difference scheme in the y. This means the poisson equation becomes...

Hello I have a physics article who solve Poisson equation of the form: L2 ∂2f/∂x2=sinh(f) The proposed solution is: tanh(f/4)=exp(x/L) tanh(f0/4) with f0 a constant I suspect an error, something like a forgotten factor. How can I verify? (I tried but I failed) I forgot the limit...

Homework Statement Suppose that the number of asbestos particles in a sam- ple of 1 squared centimeter of dust is a Poisson random variable with a mean of 1000. What is the probability that 10 squared cen- timeters of dust contains more than 10,000 particles? Homework Equations E(aX+b) =...

Good morning PF, I'm feeling a bit doubtful about this issue. I'm working with optical detectors and I have to characterize them in terms of quantum efficiency and other similar things. Now suppose my detector is, ideally, a single large pixel, which I illuminate for a specific time. Then I...

Hi, I have a simple/fast question... Can you reliably use a Poisson function to fit on data that seem to be Gaussian distributed (although that is due to the large number of the mean)?

Hello, I'm about elaborating a discrete mass-spring model to describe the vibration of a thin isotropic plate. For the flexion i choose a kind of spiral spring in the two directions X and Y: so the momentums will be Mx= Cbx.(Delta Thêta) ; My = Cby.(Dela Psi). and the energies: Eb =...

X = # of cars that pass in one hour E(X) = λ = n * p λ cars/1hour = 60min/hour * (λ/60) cars/min In this old video (5:09) on poisson process Sal asks: "What if more than one car passes in a minute?" "We call it a success if one car passes in one minute, but even if 5 cars pass, it counts as 1...

Homework Statement Non-Zero Poisson Probability distributions Scenario: The following data represents the number of typographical errors (typos) a lecturer makes (per page) in a document they are producing. A document's pages was inspected and the number of typos per page was recorded...

Homework Statement Show that, quite generally, the Poisson Mass Function has the same value at λ (i.e. the average) and at (λ-1). Homework Equations The Poisson Mass Function is p(x) = [e^(-λ) * λ^(x)]/(x!) The Attempt at a Solution I started out by plugging in λ-1 into the equation to get...

Homework Statement I need to find the variance of Y. The number of errors on a page follows a Poisson distribution with lambda = 0.40 average . Y = the number of pages without error among the first 112 pages . Homework EquationsThe Attempt at a Solution In Poisson, I know that Variance =...

I am reading a lot about how to calculate band bending from solving the Schrödinger equation and Poisson equation self-consistently. To recap some of the central ideas are: We look at the conduction band of some semiconductor. If we assume that the electrons are free electrons with some...

If we have Poisson bracket for two dynamical variables u and v, we can write as it is known ... This is for classical mechanics. If we write commutation relation, for instance, for location and momentum, we obtain Heisenberg uncertainty relation. But, what is a pedagogical transfer from...

Hey guys, what's up? I have some questions regarding the Poisson Process. I checked some threads, but not all, so forgive me if these questions have been answered before. 1)Lets say I am given some some tables or/and graphs or generally speaking some data and I am asked to find out if the...

Homework Statement 3. The Attempt at a Solution [/B] ***************************************** Can anyone possibly explain step 3 and 4 in this solution?

Homework Statement Can anybody suggest hints on how to show that x'=xcosΘ-ysinΘ, y'=xsinΘ+ycosΘ by using the infinite string of poisson brackets? Homework Equations ω→ω+a{ω,p}+a^2/2!{{ω,p},p}+... The Attempt at a Solution Sorry, I just can’t think of any way, substituting doesn’t work.

Hello In Newtonian theory Poisson's equation holds: ## \nabla ^{2} U = 4 \pi G \rho ##. So: given a density ##\rho ##, it is possible to find a potential U. On the other hand, I can choose a random function U and give it a gravitational significance if it gives, by Poisson's eq., a density...

Hello all, I have this Poisson distribution question, which I find slightly tricky, and I'll explain why. The number of car accidents in a city has a Poisson distribution. In March the number was 150, in April 120, in May 110 and in June 120. Eight days are being chosen by random, not...

Homework Statement Insects land in the soup in the manner of a Poisson process with intensity lambda. Insects are green with probability p, independent of the color of the other insects. Show that the arrival of green insects is a Poisson process with intensity p*lambda. Homework Equations3...

Homework Statement I am given a data set known to come from a poisson distribution. Homework Equations Poisson distribution The Attempt at a Solution I want to calculate the mean of the data set for use in the Poisson Distribution function. How do I best estimate this. Do I take the...

Is there a closed form expression for the sum: Σx2/n! from 0 to N for N=∞ it is an exponential but what about the finite case?

Homework Statement Say I have a detector that detects alpha-particles of some decay process. Let N be the amount of particles detected and let N be Poisson distributed. If I now define the intensity to be the amount of detected particles per second I = N/t, what would the standard deviation of...

I'm not perfectly clear on the connection between Poisson brackets in classical mechanics and commutators in quantum mechanics. For any classical mechanical system, if I can find the Poisson bracket between two physical observables, is that always the value of the corresponding commutator in the...

Homework Statement We assume that the number of structural flaws on a long wire have obey Poisson distribution law. On average we find 1 flaw every 5 meters. a) What is the probability that a 20 m long section will have maximum 2 flaws? b) We slice the wire into 1 m long sections. What is the...

Homework Statement The number of telephone calls, T, received each minute can be modeled by a Poisson distribution with a mean of 3.5. Find the probability that at least three telephone calls are received in each of two successive one-minute intervals. Homework Equations P =...

I'm not great at statistics, so I don't know where to start with this problem. It is stated as follows: The number of telephone calls, T, received each minute can be modeled by a Poisson distribution with a mean of 3.5. Find the probability that at least three telephone calls are received in...

Homework Statement A telephone operator receives four phone calls in three minutes on the average. Let a Poisson random number X denote the number of phone calls per minute to this operator. (a) Find the probability that this operator receives two phone calls in a minute. (b) Find the...

Homework Statement A teacher has an infinite flow of papers to mark. They appear in his office at random times, at an average rate of 10 a day. On average 10% of the manuscripts are free from errors. What is the probability that the teacher will see exactly one error-free manuscript (a) after...

Homework Statement I have run into a situation that my gut tells me is impossible (alright extremely unlikely) when assuming a Poisson distribution. I want to make this gut feeling more formal by testing it against a Poisson distribution. Sadly I'm not a schooled statistician. Generalised...

Homework Statement An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year. a). How many loads can be expected to occur during a 4-year period? b). What is the probability...

Homework Statement Solve the poisson eq. on R with a source in x=0. The Attempt at a Solution I haven't done this kind of thing in years, so I'm a bit rusty, but I think that this is requested: \Delta \phi = - \rho \delta(x) (Edit: no wait, I need an integral here). It doesn't seem to be...